1. Field of the Invention
The invention relates generally to the field of orthodontics and, more particularly, to computer-automated separation of a model of teeth.
2. Description of the Background Art
Tooth positioners for finishing orthodontic treatment are described by Kesling in the Am. J. Orthod. Oral. Surg. 31:297-304 (1945) and 32:285-293 (1946). The use of silicone positioners for the comprehensive orthodontic realignment of a patient""s teeth is described in Warunek et al. (1989) J. Clin. Orthod. 23:694-700. Clear plastic retainers for finishing and maintaining tooth positions are commercially available from Raintree Essix, Inc., New Orleans, La. 70125, and Tru-Tain Plastics, Rochester, Minn. 55902. The manufacture of orthodontic positioners is described in U.S. Pat. Nos. 5,186,623; 5,059,118; 5,055,039; 5,035,613; 4,856,991; 4,798,534; and 4,755,139.
Other publications describing the fabrication and use of dental positioners include Kleemann and Janssen (1996) J. Clin. Orthodon. 30:673-680; Cureton (1996) J. Clin. Orthodon. 30:390-395; Chiappone (1980) J. Clin. Orthodon. 14:121-133; Shilliday (1971) Am. J. Orthodontics 59:596-599; Wells (1970) Am. J. Orthodontics 58:351-366; and Cottingham (1969) Am. J. Orthodontics 55:23-31.
Kuroda et al. (1996) Am. J. Orthodontics 110:365-369 describes a method for laser scanning a plaster dental cast to produce a digital image of the cast. See also U.S. Pat. No. 5,605,459.
U.S. Pat. Nos. 5,533,895; 5,474,448; 5,454,717; 5,447,432; 5,431,562; 5,395,238; 5,368,478; and 5,139,419, assigned to Ormco Corporation, describe methods for manipulating digital images of teeth for designing orthodontic appliances.
U.S. Pat. No. 5,011,405 describes a method for digitally imaging a tooth and determining optimum bracket positioning for orthodontic treatment. Laser scanning of a molded tooth to produce a three-dimensional model is described in U.S. Pat. No. 5,338,198. U.S. Pat. No. 5,452,219 describes a method for laser scanning a tooth model and milling a tooth mold. Digital computer manipulation of tooth contours is described in U.S. Pat. Nos. 5,607,305 and 5,587,912. Computerized digital imaging of the jaw is described in U.S. Pat. Nos. 5,342,202 and 5,340,309. Other patents of interest include U.S. Pat. Nos. 5,549,476; 5,382,164; 5,273,429; 4,936,862; 3,860,803; 3,660,900; 5,645,421; 5,055,039; 4,798,534; 4,856,991; 5,035,613; 5,059,118; 5,186,623; and 4,755,139.
In one aspect, a computer-implemented method separates first and second portions of a tooth by defining a cutting surface intersecting the first and second portions; and applying the cutting surface to the tooth to separate the tooth into two portions.
Implementations of the aspect may include one or more of the following. The cutting surface can be curved. The cutting surface can also be expressed as a function such as a spline function. The cutting surface can be interactively adjusted, and the interactive adjustment of the cutting surface modifies the function. The process can interactively highlight the separated portion, including the border of the portion. The cutting surface can be defined by specifying one or more points on the tooth. A best fit between the points and the cutting surface can be determined. The process can also minimize the curvature along the cutting surface. The cutting surface can be adjusted by moving one or more points on the tooth, or by moving one or more nodes. Further, the cutting surface can be adjusted by specifying a point on the cutting surface and between two nodes; and adjusting the point to vary the cutting surface.
In another aspect, a computer-implemented method separates a computer model of two teeth by displaying a plane having a surface specified by a plurality of nodes; adjusting one or more nodes to modify the surface of the plane; and applying the plane to the teeth to be separated.
Implementations of the invention may include one or more of the following. A handle can be provided for each orientation of the plane to position the plane. The one or more nodes can also be adjusted by dragging and dropping the one or more nodes. The plane can be formed using one or more surface patches. The surface patches can be bicubic Bxc3xa9zier patches. Each bicubic Bxc3xa9zier patch can be described as:       S    ⁡          (              u        ,        v            )        =            ∑              i        =        0            3        ⁢                  ∑                  k          =          0                3            ⁢                        b                      i            ,            k                          ⁢                              B            k            m                    ⁡                      (            u            )                          ⁢                              B            i            n                    ⁡                      (            v            )                              
where S, u, and v are coordinates in 3D space chosen along a straight plane between the two teeth, and S is the function along the ortho-normal direction to the straight plane,
bi,k is the Bxc3xa9zier points of the patch, and
Bin(t)=nCi(1xe2x88x92t)nxe2x88x92itii=0,1, . . . , n
denotes the Bernstein polynomials.
The two joined teeth can be separated into two separated teeth by receiving an initial digital data set representing the two joined teeth; representing the two teeth as a teeth mesh; applying a cutter mesh to the teeth mesh; identifying an intersecting line between the teeth mesh and cutter mesh; and generating two separated teeth based on the intersecting line. Inside and outside meshes can be created for each tooth mesh and cutter mesh based on the intersecting line. The inside and outside meshes can be joined to create a closed surface for each of the two teeth. A common vertex between triangles on the meshes can be generated, and an intersection point from triangles sharing the common vertex can be determined. The intersection point can be connected to the common vertex to form two triangles. The intersection point can be connected to three corners of a triangle to form three triangles. Data can be obtained by scanning a physical model of the teeth. The physical model can be scanned with a destructive scanning system. The physical model can be scanned with a laser scanning system before scanning the model with the destructive scanning system. The physical models of the upper and lower teeth can be scanned in occlusion with the laser scanning system before scanning with the destructive scanning system. The volume image data can be converted into a 3D geometric model of the tooth surfaces.
In another aspect, a computer-implemented method separates a computer model of teeth by receiving a data set that contains a 3D representation of a group teeth; identifying markers in the initial data set corresponding a plane separating the teeth; determining parameters best fitting the plane to the markers; displaying the plane having a surface specified by a plurality of nodes or markers; adjusting one or more nodes or markers to modify the surface of the plane; and applying the plane to the teeth to be separated.